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Isometries on almost Ricci–Yamabe solitons
oleh: Mohan Khatri, C. Zosangzuala, Jay Prakash Singh
Format: | Article |
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Diterbitkan: | SpringerOpen 2022-10-01 |
Deskripsi
Abstract The purpose of the present paper is to examine the isometries of almost Ricci–Yamabe solitons. Firstly, the conditions under which a compact gradient almost Ricci–Yamabe soliton is isometric to Euclidean sphere $$S^n(r)$$ S n ( r ) are obtained. Moreover, we have shown that the potential f of a compact gradient almost Ricci–Yamabe soliton agrees with the Hodge–de Rham potential h. Next, we studied complete gradient almost Ricci–Yamabe soliton with $$\alpha \ne 0$$ α ≠ 0 and non-trivial conformal vector field with non-negative scalar curvature and proved that it is either isometric to Euclidean space $$E^n$$ E n or Euclidean sphere $$S^n.$$ S n . Also, solenoidal and torse-forming vector fields are considered. Lastly, some non-trivial examples are constructed to verify the obtained results.